We identify \(P\)  and \(C_+\)  as the inversion and the non-Hermitian variant of the time-reversal operators, respectively. In particular, \(C_+\)  can be identified with the \(\text{TRS}^\dag \)  symmetry in Ref. [1]}. Physically, the combined inversion and time-reversal symmetry is understood from the observation that the dissipative AB chain remains invariant by simultaneously reversing the flux and the lattice, but not either alone.
